If Iran doesn't seize the embassy they may lose face in the region and a prolonged standoff will initiate a siege-countersiege dynamic. The US may initiate a virtual investment of Iranian assets or traffic until the proxies leave the embassy.
Sieges, especially in Islamic history, often end in negotiations. This happened during the Cold War too, notably the Berlin Airlift. The essential thing to recognize is that unless the attacker takes the castle, he is effectively besieged also.
Except for the media who call the embassy attackers "mourners", most people in Iraq will see them as Iranian operatives running an extraterritorial operation in Baghdad. This imposes a fearful cost on the official govt of Iraq, which loses legitimacy with each passing day.
The Iraqi Shia politicians have to at least pretend to count. While Iran acted deniably this was possible but with things out in the open the issue of "who's in charge" will put a strain on a country recovering from civil war. The ayatollahs have put a turd in the punchbowl.
This issue, like so many others, can easily take on a life of its own, both for the US and Iran.
